Question

Capital Budgeting Example

*A proposed drone investment project for AJ-Securities has an equipment cost of $3,750,000. The cost will be depreciated straight-line to a zero salvage value over its 30 year life. The firm will also use existing equipment that has been fully depreciated but has a market value of $600,000 at the end-of-life for the project.

*The price of the drone service per customer is $3,550 a year but expect price to increase by 2.3% each year. The number of customers is expected to stay constant throughout the project life at 6,200.

*Variable costs will run $1,800 per customer per year, and expected to increase at a 1.8% rate per year.

*Fixed cost are expected to be $926,100 per year.

*The firm will also need to invest $8,500 in net working capital for the next seven years, and then increase by $10,600 in year eight and remain at this level for the life of the project.

*Marketing research for this project cost $352,500 last year, and on-going marketing ads will cost $81,200 per year.

* The risk of this drone project is different than the overall firm. Firms that only develop drone projects are: (1) Drone City that has a beta of 3.2 with Debt to Equity ratio (D/E) of 2; SS Service that has a beta of 2.7 with a (D/E) of 1.5; New Wave Securities with a beta of 2.5 and a (D/E) of 1.

*The current capital structure is: debt of 500,000 bonds at a price of $980 each with semi-annual compounding for thirty years; 1,550,000 shares of common stock currently trading for $36 per share; and Preferred Stock of 800,000 shares selling for $46 a share with annual dividends of $2.75. The coupon rate on the bonds is 6%. Next year, the firm will change the capital structure to 40% debt, 50% common stock, and 10% preferred stock.

*The US T-bill rate is 2.9%, the beta for AJ-Securities is 2.2, and the current return to the S&P500 is 12%. The corporate marginal tax rate is 33% while the average tax rate is 28%.

(A.) What are the cash flows from assets for the project?   

(B.)What is the cost of equity for this project?

(C.) What is the cost of debt for this project?

(D.) What is the cost of capital for this project?

(E.) What is the NPV of this project?

(F.) What is the Payback Period?

(G.) What is the Profitability Index?

(H.) What is the IRR?

(I.) Should you accept or reject this project? Assume the payback cutoff is 4 years.

Answer 1

(A)

The cash flows are calculated as below :

Variable costs in year 1 = 1800 * 6200. These are increased by 1.8% each year

Cash inflow from drone service in year 1 =3500*6200. This is increased by 2.3% each year

Depreciation tax shield = Equipment cost / useful life * average tax rate, which is $3,750,000 / 30 * 28%. Depreciation can be deducted from income for tax purposed and this results in reduced tax outflow. Hence this is treated as a cash inflow.

Cash flows are :

Year	Description	Cash Outflow				Cash Inflow			Net Cash Flow
		Investments	Variable Costs	Fixed Costs	Marketing	Drone Service	Depreciation Tax Shield	Other
0	Equipment Cost	($3,750,000)							($3,750,000)
0	Working Capital	($8,500)							($8,500)
1			($11,160,000)	($926,100)	($81,200)	$22,010,000	$35,000		$9,877,700
2			($11,360,880)	($926,100)	($81,200)	$22,516,230	$35,000		$10,183,050
3			($11,565,376)	($926,100)	($81,200)	$23,034,103	$35,000		$10,496,427
4			($11,773,553)	($926,100)	($81,200)	$23,563,888	$35,000		$10,818,035
5			($11,985,477)	($926,100)	($81,200)	$24,105,857	$35,000		$11,148,081
6			($12,201,215)	($926,100)	($81,200)	$24,660,292	$35,000		$11,486,777
7			($12,420,837)	($926,100)	($81,200)	$25,227,479	$35,000		$11,834,342
8			($12,644,412)	($926,100)	($81,200)	$25,807,711	$35,000		$12,190,998
8	Working Capital	($10,600)							($10,600)
9			($12,872,011)	($926,100)	($81,200)	$26,401,288	$35,000		$12,556,976
10			($13,103,708)	($926,100)	($81,200)	$27,008,517	$35,000		$12,932,510
11			($13,339,574)	($926,100)	($81,200)	$27,629,713	$35,000		$13,317,839
12			($13,579,687)	($926,100)	($81,200)	$28,265,197	$35,000		$13,713,210
13			($13,824,121)	($926,100)	($81,200)	$28,915,296	$35,000		$14,118,875
14			($14,072,955)	($926,100)	($81,200)	$29,580,348	$35,000		$14,535,093
15			($14,326,269)	($926,100)	($81,200)	$30,260,696	$35,000		$14,962,128
16			($14,584,141)	($926,100)	($81,200)	$30,956,692	$35,000		$15,400,251
17			($14,846,656)	($926,100)	($81,200)	$31,668,696	$35,000		$15,849,740
18			($15,113,896)	($926,100)	($81,200)	$32,397,076	$35,000		$16,310,880
19			($15,385,946)	($926,100)	($81,200)	$33,142,209	$35,000		$16,783,963
20			($15,662,893)	($926,100)	($81,200)	$33,904,480	$35,000		$17,269,287
21			($15,944,825)	($926,100)	($81,200)	$34,684,283	$35,000		$17,767,158
22			($16,231,832)	($926,100)	($81,200)	$35,482,021	$35,000		$18,277,889
23			($16,524,005)	($926,100)	($81,200)	$36,298,108	$35,000		$18,801,803
24			($16,821,437)	($926,100)	($81,200)	$37,132,964	$35,000		$19,339,227
25			($17,124,223)	($926,100)	($81,200)	$37,987,022	$35,000		$19,890,500
26			($17,432,459)	($926,100)	($81,200)	$38,860,724	$35,000		$20,455,965
27			($17,746,243)	($926,100)	($81,200)	$39,754,520	$35,000		$21,035,978
28			($18,065,675)	($926,100)	($81,200)	$40,668,874	$35,000		$21,630,899
29			($18,390,857)	($926,100)	($81,200)	$41,604,259	$35,000		$22,241,101
30			($18,721,893)	($926,100)	($81,200)	$42,561,156	$35,000		$22,866,964
30	Equipment market value							$600,000	$600,000

(b) To calculate the cost of equity, we first calculate the unlevered beta of firms that develop only drone projects

β Unlevered = β(Levered) / [1+ (Debt/Equity) (1-T)]

average beta of firms = (3.2 + 2.7 + 2.5) / 3, which is 2.8

average D/E ratio = (2 + 1.5 + 1), which is 1.5

average tax rate is 28%, or 0.28

β Unlevered = 2.8 / (1 + (1.5)(1 - 0.28) ==> 1.35

Now, we relever the beta using the D/E ratio of AJ Securites

D/E ratio next year = 40% debt / 50% common stock ==> 0.40 / 0.50 ==> 0.80

β Levered = β(Unlevered) x [1+(Debt/Equity) (1-T)]

β Levered = 1.35 * (1 + (0.80)(1 - 0.28) ==> 2.13

Cost of equity = risk free rate + (beta)(equity market portfolio return - risk free rate)

We use the beta calculated above, and not the existing beta of 2.2 given in the question. This is because the risk for this project is different from the risk of the overall firm

Cost of equity = 2.9% + (2.13)(12% - 2.9%) ==> 22.28%

(c) cost of debt = current yield on bonds

current yield = coupon payment / current price

current yield, or cost of debt = $60 / $980 ==> 0.0612, or, 6.12%

(d) cost of capital = (weight of debt * cost of debt) + (weight of equity * cost of equity) + (weight of preferred stock * cost of preferred stock)

cost of preferred stock = dividend / current price ==> $2.75 / $46 ==>  0.0598, or 5.98%

cost of capital = (40% * 6.12%) + (50% * 22.28%) + (10% * 5.98%)

cost of capital = 14.19%

(e) we calculate NPV by discounting the net cash flows back to the present at the discount rate of 14.19%, which is the cost of capital

PV of net cash flow in Year X = net cash flow / (1 + 0.1419)^X

NPV is the sum of PVs

NPV = $80,600,866